Another in the best-arm identification literature constrains is called the “fixed confidence” setting. This formulation places a uniform constraint on the probability of incorrect selection, restricting to algorithms satisfying \(\sup _{\theta _0} \mathbb {P}( I_{\tau }^+ \ne I^*(\theta _0) \mid \theta = \theta _0) \leqslant \delta \) . For problems without constants, [1]} and [2]} characterize the minimal expected sample size \(\mathbb {E}[ \tau \mid \theta =\theta _0]\)  attainable by algorithms satisfying this constraint in the limit where \(\delta \rightarrow 0\) . In a special case of our formulation without contexts, the complexity measure \(\Gamma _{\theta }\)  and optimal sampling proportions \(p^*(\theta )\)  match those in [1]}, [2]} and also the results regarding posterior convergence in [5]}.
